10. Comparing Means Using Repeated
Measures ANOVA
Objectives
Calculate repeated measures ANOVAs
Calculate effect size
Conduct multiple comparisons
Graphically illustrate mean differences
Repeated measures ANOVAs are used to examine mean differences in related
variables. Typically the independent variable is either time (e.g., depression is measured
in the same group of people at multiple points in time) or condition (e.g., each subject
receives every condition). In SPSS, we will use the General Linear Model to calculate
repeated measures ANOVAs.
Using GLM Repeated Measures to Calculate Repeated Measures ANOVAs
Let’s begin with an example from the exercises in Chapter 18 in the
Fundamentals book. In this example, the duration of migraine headaches was recorded
among the same group of individuals over 5 weeks. The first 2 weeks were part of a
baseline period and the final 3 weeks were part of an intervention period in which
subjects were trained to apply relaxation techniques. In this case, the independent
variable is time and the dependent variable is headache duration.
Open migraines.sav.
Select Analyze/General Linear Model/Repeated Measures.
The default for Within-Subject
Factor Name is Factor 1. Let’s
change it to Time by typing in the
box. Specify 5 for Number of Levels
since there are 5 weeks and then click
Add. Next, click Define.
As you can see, there are 5 spots
under Within-Subject Variables.
We need to indicate that each week
is a variable, and we want to list
them in the right order. You can
either select them one at a time and
arrow them into the variable list, or
you can select them all by holding
down the control button while you
select each one, and arrow them in
at once. This is a simple design, so
there are no Between-Subject
Factors or Covariates. Click Plots.
Select time as the Horizontal Axis or Y
Axis. Then click Add, and Continue. This
will plot the mean duration of headaches for
each week for us. In the main dialog box,
click Options.
Under Display, select Descriptive
Statistics, Estimates of Effect Size, and
Observed Power. Then click Continue.
And finally, Ok. The output follows.
Descriptive Statistics
Mean
headache
duration week 1
headache
duration week 2
headache
duration week 3
headache
duration week 4
headache
duration week 5
Std. Deviation
N
20.78
7.17
9
20.00
10.22
9
9.00
3.12
9
5.78
3.42
9
6.78
4.12
9
Profile Plots
Estimated Marginal Means of MEASURE_1
30
Estimated Marginal Means
20
10
0
1
2
3
4
5
TIME
As you can see, there is a lot of output, much of which we can ignore for our
purposes. Specifically, ignore Multivariate Tests, Tests of Within-Subjects Contrasts,
and Tests of Between Subjects Effects. The multivariate tests are another way to run the
analysis, and often not a good way. The contrasts give tests of linear and quadratic trends
in the data, and are not particularly of interest here. There are no between subjects
factors, so that output is not of interest. Now, let’s look at the rest and compare it to the
answers in the text. First, you can compare the mean scores for each week by looking at
the Descriptive Statistics table. The next piece is Mauchly’s Test of Sphericity, which
tests the assumption that each of the time periods is approximately equally correlated
with every other score. As noted in the text, when this assumption is violated, various
corrections are applied. Also, as noted in the text, this is not a particularly good test, but it
is about the best we have. The next table of interest, Tests of Within-Subjects Effects,
is what we really want to see. Compare the textbook values to those listed in the rows
marked Sphericity Assumed, because they were calculated the same way. As you can
see, they are in agreement.
Now, note the values for eta squared and observed power. Can you interpret
them? Nearly 73% of the variability in headache duration is accounted for by time.
Observed power is based on the assumption that the true difference in population means
is the difference implied by the sample means. Typically, we want to calculate power
going into an experiment based on anticipated or previous effect size in other similar
studies. This is useful in making decisions about sample size. So, observed power
calculated here is not particularly useful.
The graph is a nice illustration of the mean headache duration over time. You
may want to edit it to include more meaningful labels and a title.
Now, we need to calculate multiple comparisons to help us understand the
meaning of the significant effect of time on headache duration.
Multiple Comparisons
Let’s just try one of the possible multiple comparisons, the comparison between
the overall baseline mean and the overall training mean. We can use SPSS
Transform/Compute to calculate these averages for us rather than doing it manually.
In the Data Editor window, select Transform/Compute.
Type baseline under Target
Variable. The under the list of
Functions, select MEAN and
arrow it into the dialog box. We
need to tell SPSS from what
variables to calculate the mean.
Select week1 and week2 to replace
the 2 question marks. Make sure
they are separated by a comma and
the question marks are gone.
Then, click Ok.
Look at the new variable in the Data Editor. Does it look right?
Click Transform/Compute again. Click Reset to remove the previous information.
Name the next Target Variable training. Select MEAN again. Specify, week3,
week4, and week5. Make sure the question marks are gone and commas separate each
variable. Then, click Ok. Check out your new variable.
Use Analyze/Descriptives to calculate the means for baseline and training. The data
follow.
As you can see, the means are consistent with those reported in the textbook. Now, you
can apply formula using MSerror from the ANOVA. The computations follow.
t
20.39  7.17
13.20

 9.14
1
1
2.086
22.53(  )
18 27
Although some hand calculations are required, we saved time and reduced the likelihood
of making errors by using SPSS to compute the new mean scores for baseline and
training for us.
In this chapter, you learned to use the General Linear Model to calculate repeated
measures ANOVAs. In addition, you learned to use SPSS to calculate new means for use
in multiple comparisons. Try the following exercises to help you become more familiar
with the process.
Exercises
The following exercises are based on Eysenck repeated.sav.
1. Use a repeated measures ANOVA to examine the effect of condition on recall.
Compare your results to those presented in the textbook in Section 18.7.
2. Use SPSS to calculate the effect size of condition.
3. Plot the mean difference in recall by conditions.
4. Use SPSS to calculate the mean of counting, rhyming, adjective, and intentional
and label it lowproc for lower processing. Then use the multiple comparisons
procedure explained in the textbook to compare the mean recall from the lower
processing conditions to the mean recall for imagery, which was the highest
processing condition. Write a brief statement explaining the results.